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Select all of the equations below that are equivalent to:\newline38n=92-38n = 92\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A) 38n23=4-\frac{38n}{-23} = -4\newline(B) 38n23=4-\frac{38n}{23} = 4\newline(C) 19n=92219n = \frac{92}{-2}\newline(D) 38n23=2-\frac{38n}{23} = 2

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Q. Select all of the equations below that are equivalent to:\newline38n=92-38n = 92\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A) 38n23=4-\frac{38n}{-23} = -4\newline(B) 38n23=4-\frac{38n}{23} = 4\newline(C) 19n=92219n = \frac{92}{-2}\newline(D) 38n23=2-\frac{38n}{23} = 2
  1. Analyze choice (A): First, let's analyze choice (A) 38n23=4\frac{-38n}{-23} = -4. To check if this equation is equivalent to 38n=92-38n = 92, we can multiply both sides of the equation 38n23=4\frac{-38n}{-23} = -4 by 23-23 to see if we get 38n=92-38n = 92. 38n23×(23)=4×(23)\frac{-38n}{-23} \times (-23) = -4 \times (-23) 38n=92-38n = 92 This shows that choice (A) is equivalent to the original equation.
  2. Check equivalence for choice (A): Now, let's analyze choice (B) 38n23=4\frac{-38n}{23} = 4. To check if this equation is equivalent to 38n=92-38n = 92, we can multiply both sides of the equation 38n23=4\frac{-38n}{23} = 4 by 2323 to see if we get 38n=92-38n = 92. 38n23×23=4×23\frac{-38n}{23} \times 23 = 4 \times 23 38n=92-38n = 92 This shows that choice (B) is not equivalent to the original equation because the sign on the right side does not match; it should be negative.

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